For a 4-unit class like Statistics, students should spend average of 12 hours studyingfor the class. A survey was done on 25 students, and the distribution of total studyhours per week is bell-shaped with a mean of 13 hours and a standard deviation of 2.7hoursUse the Empirical Rule to answer the following questionsa) 68% of the students spend betweenhours andhours on Statisticseach weekhours andb) 95% of the students spend betweenhours on Statisticseach weekc) 99.7% of the students spend betweenhours andhours on Statisticseach week.

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Asked Nov 17, 2019
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For a 4-unit class like Statistics, students should spend average of 12 hours studying
for the class. A survey was done on 25 students, and the distribution of total study
hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 2.7
hours
Use the Empirical Rule to answer the following questions
a) 68% of the students spend between
hours and
hours on Statistics
each week
hours and
b) 95% of the students spend between
hours on Statistics
each week
c) 99.7% of the students spend between
hours and
hours on Statistics
each week.
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For a 4-unit class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on 25 students, and the distribution of total study hours per week is bell-shaped with a mean of 13 hours and a standard deviation of 2.7 hours Use the Empirical Rule to answer the following questions a) 68% of the students spend between hours and hours on Statistics each week hours and b) 95% of the students spend between hours on Statistics each week c) 99.7% of the students spend between hours and hours on Statistics each week.

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Expert Answer

Step 1

68-95-99.7-rule:

Let X be an observation from a bell shaped distribution, having mean x-bar and sample standard deviation s, then according to the 68-95-99.7-rule, approximately 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean respectively. That is,

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P(-1s X+1s) 0.68 P(-2sX2s) 0.95 P(-3sX3s) 0.997

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Step 2

a.

It is given that the distribution of total study hours per week is bell-shaped with mean 13 hours and standard deviation of 2.7 hours.

It is known that 68% of the data lies within one standard deviations of the mean.

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ts 13 2.7 -[13-2.7,13+2.7] (10.3,15.7) Hence, 68% of the students spend between 10.3 hours and 15.7 hours on statistics each week

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Step 3

b.

It is known that 95% of the data lies within two standard deviations of the mean. ...

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t 2s 13 2(2.7) [13-5.4,13+5.4 -(7.6,18.4) Hence, 95% of the students spend between 7.6 hours and 18.4 hours on statistics each week

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